A few categories of theists do come to mind.
On one "non-extreme" there are apatheists who simply happen to also be theists.
On the extreme, there are the Acolytes of the True Faith, a group I would probably belong to if I believed in God at all.
Those are people who go beyond simply having strong belief in the existence of God, who also have for some reason or another a need to convince others to renounce their mistaken ways, supposedly for their own good. Many end up using their beliefs as justification for disrespecting the personal space of others. It happens with fire-and-brimstone preachers, but also with parents and relatively well-meaning people that are simply too lazy, too weak or too addicted to their abusive ways.
It is only human to feel tempted to influence other people. But it is considerably easier to fall prey to that temptation once one convinces himself to be doing God's work.
We already have several terms for those people.